415432800 has 216 divisors, whose sum is σ = 1519887096. Its totient is φ = 110730240.

The previous prime is 415432799. The next prime is 415432807. The reversal of 415432800 is 8234514.

415432800 is a `hidden beast` number, since 41 + 543 + 2 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (216).

It is a super-2 number, since 2×415432800² = 345168822631680000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415432807) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 193332 + ... + 195468.

Almost surely, 2^415432800 is an apocalyptic number.

415432800 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 415432800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (759943548).

415432800 is an abundant number, since it is smaller than the sum of its proper divisors (1104454296).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

415432800 is a wasteful number, since it uses less digits than its factorization.

415432800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2172 (or 2147 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 415432800 is about 20382.1686775475. The cubic root of 415432800 is about 746.1628013565.

The spelling of 415432800 in words is "four hundred fifteen million, four hundred thirty-two thousand, eight hundred".